Finite Group Databasebeta

← #26217976

Subgroups — #26217976

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic, complemented
2C2×#15689630C211yesmaximal, characteristic
3C2×#15689124C211yesmaximal, characteristic, complemented
4C2×#15688980C211yesmaximal, characteristic, complemented
5#20243823C212yesmaximal, complemented
6#20243818C212yesmaximal, complemented
7#20243813C212yesmaximal, complemented
8#20243808C212yesmaximal, complemented
9#20243108C211yesmaximal, characteristic, complemented
10#20243107C211yesmaximal, characteristic, complemented
11C2×C47×#417C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×#10625329C2211yescharacteristic
14C22×#10625324C2212yes—
15C2×M16×D47—24no—
16C2×M16×D47—24no—
17C2×M16×D47—24no—
18C22×C8×D47C2212yes—
19#15689630—24no—
20#15689630C418yescomplemented
21C2×#13094005—21no—
22C2×#13094000C2211yescharacteristic
23C2×#13094000C2211yescharacteristic
24C2×#13093995C2211yescharacteristic
25C2×#13093995C2211yescharacteristic
26C2×#13093992—21no—
27C2×C4×C22⋊D47—21no—
28C2×C4×C22⋊D47—21no—
29C2×#13093983C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C22×(C2×D47)⋊C4—21no—
32#15689124—24no—
33C2×#13093948C2212yescomplemented
34C2×#13093945C2212yescomplemented
35#15688980—21no—
36#15688980—21no—
37#15688980C2212yes—
38#15688980C2212yes—
39C2×C47⋊#95—21no—
40#15688886C2212yescomplemented
41#15688886C2212yescomplemented
42#15688885C2212yescomplemented
43#15688885C2212yescomplemented
44C22×#41×C47C2211yescharacteristic
45C22×M16×C47C2211yescharacteristic
46C22×C4⋊C4×C47C2211yescharacteristic
47C47×#417—24no—
48C2×#103×C47C2212yescomplemented
49C2×#102×C47C2212yescomplemented
50C24×D47D411yescharacteristic
51C22×C22⋊D47—21no—
52C22×C22⋊D47—21no—
53C23×Dic47—21no—
54C23×Dic47D411yescharacteristic
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47C2×C414yes—
60C22×C4×D47D411yescharacteristic
61C22×C4×D47D411yescharacteristic
62C22×C4×D47D414yes—
63C22×C4×D47C2311yescharacteristic
64C22×C4×D47C2311yescharacteristic
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329D414yescomplemented
68C2×#10625324—24no—
69C2×#10625324—24no—
70C2×#10625324—24no—
71M16×D47—232no—
72C22×C47⋊C8C2312yes—
73C2×C8×D47—24no—
74C2×C8×D47—24no—
75C2×C8×D47—24no—
76#13094005—28no—
77#13094000—22no—
78#13094000—22no—
79#13094000C2×C414yescomplemented
80#13094000C2×C414yescomplemented
81#13093995—22no—
82#13093995—22no—
83#13093995C2×C414yescomplemented
84#13093995C2×C414yescomplemented
85#13093992—28no—
86C4×C22⋊D47—28no—
87C4×C22⋊D47—28no—
88#13093983—22no—
89#13093983C2×C414yes—
90C2×C4⋊Dic47—22no—
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2312yes—
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—22no—
104C2×(C2×D47)⋊C4—22no—
105C2×(C2×D47)⋊C4—44no—
106C2×C4×Dic47—21no—
107#13093948—24no—
108#13093945—24no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47—22no—
114C2×#41×C47—22no—
115C2×#41×C47—22no—
116C2×#41×C47C2×C414yes—
117C22×Q8×C47C2311yescharacteristic
118C22×D4×C47—21no—
119C22×D4×C47C2311yescharacteristic
120C23×C4×C47—21no—
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C2×M16×C47—22no—
124C2×M16×C47—22no—
125C2×M16×C47D414yescomplemented
126C22×C8×C47C2312yes—
127C2×C4⋊C4×C47—22no—
128C2×C4⋊C4×C47—22no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47C2312yes—
131#103×C47—24no—
132#102×C47—24no—
133C24×C47—21no—
134C24×C47C2×D411yescharacteristic
135C23×D47—22no—
136C23×D47—22no—
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—41no—
140C23×D47—41no—
141C23×D47C22⋊C414yes—
142C23×D47C2×D411yescharacteristic
143C23×D47C2×D411yescharacteristic
144#41×C47—28no—
145#41×C47—28no—
146#41×C47—44no—
147#41×C47—44no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47C22×C412yes—
154C2×D4×C47—24no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—42no—
161C2×D4×C47—42no—
162C2×D4×C47C22×C412yes—
163C22×C4×C47—21no—
164C22×C4×C47—24no—
165C22×C4×C47—22no—
166C22×C4×C47—42no—
167C22×C4×C47—42no—
168C22×C4×C47—42no—
169C22×C4×C47—42no—
170C22×C4×C47—42no—
171C22×C4×C47C22×C412yes—
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2×D412yes—
175C22×C4×C47C2×D412yes—
176C22×C4×C47#4112yes—
177C22×C4×C47#4112yes—
178C22×C4×C47C2411yescharacteristic
179C2×C22⋊D47—24no—
180C2×C22⋊D47—24no—
181C2×C22⋊D47—42no—
182C2×C22⋊D47—42no—
183C2×C22⋊D47—42no—
184C2×C22⋊D47—42no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—22no—
190C22×Dic47—42no—
191C22×Dic47—42no—
192C22×Dic47—42no—
193C22×Dic47C22⋊C414yes—
194C22×Dic47C2×D411yescharacteristic
195C22×Dic47C2×D411yescharacteristic
196C2×C4×D47—28no—
197C2×C4×D47—28no—
198C2×C4×D47—28no—
199C2×C4×D47—22no—
200C2×C4×D47—22no—
201C2×C4×D47—22no—
202C2×C4×D47—22no—
203C2×C4×D47—28no—
204C2×C4×D47—21no—
205C2×C4×D47—21no—
206C2×C4×D47—21no—
207C2×C4×D47—21no—
208C2×C4×D47—21no—
209C2×C4×D47—21no—
210C2×C4×D47—21no—
211C2×C4×D47—21no—
212C2×C4×D47C22⋊C414yes—
213C2×C4×D47C22⋊C414yes—
214C2×C4×D47C22×C412yes—
215C2×C4×D47C22×C412yes—
216C2×C4×D47C2×D412yes—
217C2×C4×D47C2×D412yes—
218M16×C47—28no—
219C2×C8×C47—22no—
220C2×C8×C47—22no—
221C2×C8×C47C2×D414yes—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—22no—
224C4⋊C4×C47—42no—
225C22⋊Dic47—24no—
226C22⋊Dic47—24no—
227C22⋊Dic47—24no—
228(C2×D47)⋊C4—24no—
229(C2×D47)⋊C4—24no—
230(C2×D47)⋊C4—44no—
231(C2×D47)⋊C4—44no—
232C4⋊Dic47—21no—
233C4⋊Dic47—21no—
234C4⋊Dic47—22no—
235C4⋊Dic47—22no—
236C4⋊Dic47—42no—
237C4⋊Dic47C22×C412yes—
238C4⋊Dic47C22×C412yes—
239Dic47⋊C4—24no—
240Dic47⋊C4—24no—
241C4×Dic47—24no—
242#10625329—28no—
243C2×C47⋊C8—22no—
244C2×C47⋊C8—22no—
245C2×C47⋊C8C2×D414yes—
246#10625324—216no—
247C8×D47—216no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—22no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47C2×C22⋊C412yes—
260C23×C47#12112yes—
261C23×C47#12112yes—
262C23×C47C22×D411yescharacteristic
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—28no—
274C22×D47—28no—
275C22×D47—44no—
276C22×D47—44no—
277C22×D47—44no—
278C22×D47—44no—
279C22×D47—44no—
280C22×D47C2×C22⋊C412yes—
281C22×D47C2×C22⋊C412yes—
282C22×D47AGL(1,ℤ/8)12yes—
283C22×D47#13712yes—
284Q8×C47—22no—
285Q8×C47—22no—
286Q8×C47—41no—
287Q8×C47—41no—
288D4×C47—22no—
289D4×C47—22no—
290D4×C47—48no—
291D4×C47—41no—
292D4×C47—41no—
293C2×C4×C47—22no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—48no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—84no—
301C2×C4×C47C2×C22⋊C412yes—
302C2×C4×C47C4×D414yes—
303C2×C4×C47C4×D414yes—
304C2×C4×C47#12014yes—
305C2×C4×C47#12112yes—
306C2×C4×C47#12112yes—
307C2×C4×C47#12314yes—
308C2×C4×C47C23×C411yescharacteristic
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4111yescharacteristic
313C2×C4×C47C2×#4111yescharacteristic
314C22⋊D47—48no—
315C22⋊D47—48no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—28no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—84no—
331C2×Dic47C2×C22⋊C412yes—
332C2×Dic47C2×C22⋊C412yes—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—22no—
341C4×D47—28no—
342C4×D47—28no—
343C8×C47—24no—
344C47⋊C8—24no—
345#20971—471nomaximal, Sylow
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—81no—
359C22×C47#38614yes—
360C22×C47C22×C22⋊C411yescharacteristic
361C22×C47C2×#12111yescharacteristic
362C22×C47C2×#12111yescharacteristic
363C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C47C2×#13711yescharacteristic
365C22×C47#57511yescharacteristic
366C22×C47#57511yescharacteristic
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—416no—
377C2×D47—41no—
378C2×D47—41no—
379C2×D47—41no—
380C2×D47—41no—
381C2×D47#41714yescomplemented
382C4×C47—42no—
383C4×C47—82no—
384C4×C47#38614yes—
385C4×C47C2×C4×D411yescharacteristic
386C4×C47C2×C4×D411yescharacteristic
387C4×C47C2×#12011yescharacteristic
388C4×C47C2×#12311yescharacteristic
389Dic47—22no—
390Dic47—22no—
391Dic47—42no—
392Dic47—42no—
393Dic47—82no—
394C23×M16—471no—
395C2×#525—471no—
396C2×#417—471no—
397C2×#417D4711yescharacteristic, complemented
398C2×#380—471no—
399#1895—472no—
400#1894—472no—
401#1893—472no—
402#1892—472no—
403#1736—471no—
404#1736—471no—
405C2×C47—24no—
406C2×C47—82no—
407C2×C47C2×#38611yescharacteristic
408C2×C47C2×#41711yescharacteristic
409C2×C47#289611yescharacteristic
410C2×C47#305511yescharacteristic
411C2×C47#305511yescharacteristic
412C2×C47#305611yescharacteristic
413C2×C47#305611yescharacteristic
414D47—24no—
415D47—42no—
416C22×#41C2×D4711yescharacteristic
417C24×C4—471no—
418C22×M16—471no—
419C22×M16—472no—
420C22×M16—944no—
421C22×M16—944no—
422C22×M16—944no—
423C22×M16C2×D4711yescharacteristic
424C23×C8—472no—
425#525—478no—
426#525—944no—
427C2×#123—941no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×#121—471no—
431C2×#121—471no—
432C2×#120—941no—
433C2×C4×D4—941no—
434C2×C4×D4—941no—
435C2×#117—471no—
436C22×C4⋊C4—471no—
437C22×C4⋊C4C2×D4711yescharacteristic
438C22×C22⋊C4—941no—
439#417—24no—
440#417—944no—
441C2×#103—472no—
442C2×#103C2×D4712yescomplemented
443C2×#102—472no—
444C2×#102C2×D4712yescomplemented
445#380—472no—
446#380—472no—
447#380—941no—
448#380—941no—
449C2×#95—941no—
450#340—472no—
451#340—472no—
452#340—472no—
453#340—472no—
454C47#2097111yescharacteristic, complemented, Sylow
455C25—471no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41C4×D4714yes—
462C22×Q8C22×D4711yescharacteristic
463C22×D4—21no—
464C22×D4—941no—
465C22×D4—941no—
466C22×D4C22×D4711yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—471no—
470C23×C4—474no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—474no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—942no—
477C23×C4—942no—
478C23×C4—942no—
479C23×C4—942no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482C2×M16—22no—
483C2×M16—22no—
484C2×M16—474no—
485C2×M16—944no—
486C2×M16—944no—
487C2×M16—9432no—
488C2×M16—942no—
489C2×M16—942no—
490C2×M16—944no—
491C2×M16C22⋊D4714yescomplemented
492C22×C8—472no—
493C22×C8—944no—
494C22×C8—944no—
495C22×C8—944no—
496C22×C8C22×D4712yes—
497#123—948no—
498C22⋊Q8—474no—
499C22⋊Q8—474no—
500C22⋊Q8—942no—
501C22⋊Q8—942no—
502#121—474no—
503#121—474no—
504#121—942no—
505#121—942no—
506#120—948no—
507C4×D4—948no—
508C4×D4—948no—
509#117—474no—
510#117—942no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—472no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—942no—
520C2×C4⋊C4—942no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4C22×D4712yes—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—942no—
529C2×C22⋊C4—942no—
530C2×C22⋊C4—1884no—
531C2×C42—941no—
532#103—24no—
533#103—944no—
534#102—24no—
535#102—944no—
536#95—942no—
537#95—942no—
538C24—21no—
539C24—471no—
540C24—471no—
541C24—474no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24—942no—
546C24—1881no—
547C24—1881no—
548C24D4×D4711yescharacteristic
549#41—28no—
550#41—28no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C2×C4×D4712yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—944no—
568C2×D4—944no—
569C2×D4—1882no—
570C2×D4—1882no—
571C2×D4—1882no—
572C2×D4—1882no—
573C2×D4C2×C4×D4712yes—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—474no—
583C22×C4—471no—
584C22×C4—471no—
585C22×C4—474no—
586C22×C4—474no—
587C22×C4—472no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—948no—
594C22×C4—948no—
595C22×C4—948no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—948no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—942no—
612C22×C4—1882no—
613C22×C4—1882no—
614C22×C4—1882no—
615C22×C4C2×C4×D4712yes—
616C22×C4#1062535012yes—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4712yes—
619C22×C4D4×D4712yes—
620C22×C4#1062535212yes—
621C22×C4C2×C22⋊D4712yes—
622C22×C4C23×D4711yescharacteristic
623M16—28no—
624M16—9416no—
625M16—948no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—474no—
629C2×C8—9416no—
630C2×C8—942no—
631C2×C8—942no—
632C2×C8C2×C22⋊D4714yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—42no—
636C4⋊C4—472no—
637C4⋊C4—472no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—941no—
641C4⋊C4—941no—
642C4⋊C4—942no—
643C4⋊C4—942no—
644C4⋊C4—1882no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C22⋊C4—1884no—
651C22⋊C4—1884no—
652C42—944no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—472no—
665C23—472no—
666C23—472no—
667C23—472no—
668C23—948no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—948no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23—941no—
680C23—1884no—
681C23—1884no—
682C23—1884no—
683C23—1884no—
684C23—1884no—
685C23C22⋊C4×D4712yes—
686C23#1309399512yes—
687C23#1309399712yes—
688C23C2×D4×D4711yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—1888no—
699D4—1888no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—48no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—948no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—948no—
716C2×C4—948no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—3764no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1881no—
735C2×C4C22⋊C4×D4712yes—
736C2×C4(C22⋊D47)⋊C414yes—
737C2×C4C4×C22⋊D4714yes—
738C2×C4#1309399214yes—
739C2×C4#1309399512yes—
740C2×C4#1309399712yes—
741C2×C4#1309400614yes—
742C2×C4C22×C4×D4711yescharacteristic
743C2×C4C2×D4×D4711yescharacteristic
744C2×C4C2×D4×D4711yescharacteristic
745C2×C4C22×C22⋊D4711yescharacteristic
746C2×C4C2×#1062535211yescharacteristic
747C2×C4C2×#1062535011yescharacteristic
748C8—24no—
749C8—944no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—474no—
764C22—942no—
765C22—942no—
766C22—942no—
767C22—942no—
768C22—942no—
769C22—942no—
770C22—942no—
771C22—942no—
772C22—942no—
773C22—18816no—
774C22—1881no—
775C22—1881no—
776C22—1881no—
777C22—1881no—
778C22#1568899914yes—
779C22C2×C22⋊C4×D4711yescharacteristic
780C22C2×#1309399511yescharacteristic
781C22C2×#1309399711yescharacteristic
782C22AGL(1,ℤ/8)×D4711yescharacteristic
783C22#137×D4711yescharacteristic
784C22#1568991911yescharacteristic
785C22#1568992211yescharacteristic
786C4—42no—
787C4—82no—
788C4—942no—
789C4—942no—
790C4—3762no—
791C4—1882no—
792C4—1882no—
793C4#1568899914yes—
794C4C2×(C22⋊D47)⋊C411yescharacteristic
795C4C2×C4×C22⋊D4711yescharacteristic
796C4C2×#1309399211yescharacteristic
797C4C2×#1309400611yescharacteristic
798C2—24no—
799C2—82no—
800C2—944no—
801C2—1882no—
802C2C2×#1568899911yescharacteristic
803C2#417×D4711yescharacteristic
804C2#2025190411yescharacteristic
805C2#2025300111yescharacteristic
806C2#2025301011yescharacteristic
807C2#2025301211yescharacteristic
808C2#2025302111yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
prime radicalC2×#15689630C2
cosocleC22×C4×C47C24
hypercenterC2×#417D47
hypocenterC47#20971
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×M16×D47C2semidirect
3. C2×#15689124C2semidirect
4. C2×#15688980C2semidirect
5. #20243823C2semidirect
6. #20243818C2semidirect
7. #20243813C2semidirect
8. #20243808C2semidirect
9. #20243108C2semidirect
10. #20243107C2semidirect
11. C2×C47×#417C2semidirect
20. #15689630C4semidirect
33. C2×#13093948C22semidirect
34. C2×#13093945C22semidirect
40. #15688886C22semidirect
41. #15688886C22semidirect
42. #15688885C22semidirect
43. #15688885C22semidirect
48. C2×#103×C47C22semidirect
49. C2×#102×C47C22semidirect
67. C2×#10625329D4semidirect
79. #13094000C2×C4semidirect
80. #13094000C2×C4semidirect
83. #13093995C2×C4semidirect
84. #13093995C2×C4semidirect
125. C2×M16×C47D4semidirect
381. C2×D47#417semidirect
397. C2×#417D47semidirect
442. C2×#103C2×D47semidirect
444. C2×#102C2×D47semidirect
454. C47#20971semidirect
491. C2×M16C22⋊D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×M16×D472
C2×#156896302
C2×#156891242
C2×#156889802
#202438232
#202438182
#202438132
#202438082
#202431082
#202431072
C2×C47×#4172
#2097147